Question: Solve for $x$ and $y$ using elimination. ${3x-4y = 0}$ ${6x-5y = 9}$
We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Multiply the top equation by $-2$ ${-6x+8y = 0}$ $6x-5y = 9$ Add the top and bottom equations together. $3y = 9$ $\dfrac{3y}{{3}} = \dfrac{9}{{3}}$ ${y = 3}$ Now that you know ${y = 3}$ , plug it back into $\thinspace {3x-4y = 0}\thinspace$ to find $x$ ${3x - 4}{(3)}{= 0}$ $3x-12 = 0$ $3x-12{+12} = 0{+12}$ $3x = 12$ $\dfrac{3x}{{3}} = \dfrac{12}{{3}}$ ${x = 4}$ You can also plug ${y = 3}$ into $\thinspace {6x-5y = 9}\thinspace$ and get the same answer for $x$ : ${6x - 5}{(3)}{= 9}$ ${x = 4}$